How do you find the coordinates of the other endpoint of a segment with the given midpoint (-3, 7) and one endpoint of a segment (5,-1)?

Question

Avery Alexander · Accepted Answer

undefined To find the coordinates of the other endpoint of a segment, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a segment are the average of the coordinates of its endpoints.

Let's denote the coordinates of the other endpoint as (x, y). Using the midpoint formula, we can set up the following equation:

(x + 5)/2 = -3 and (y - 1)/2 = 7

Simplifying these equations, we get:

x + 5 = -6 and y - 1 = 14

Solving for x and y, we find:

x = -11 and y = 15

Therefore, the coordinates of the other endpoint of the segment are (-11, 15).

Savannah Anderson · Answer

Use the midpoint formula but solve for one of the endpoints.

The Midpoint formula is: #x_"midpoint" = (x_"endpoint" + x_"startpoint")/2# and #y_"midpoint" = (y_"endpoint" + y_"startpoint")/2# Substitute -3 for #x_"midpoint"# and 7 for #y_"midpoint"# #-3 = (x_"endpoint" + x_"startpoint")/2# and #7 = (y_"endpoint" + y_"startpoint")/2# Substitute 5 for #x_"startpoint"# and -1 for y_"startpoint": #-3 = (x_"endpoint" + 5)/2# and #7 = (y_"endpoint" -1)/2# We can solve the two equations for the endpoint: #-6 = x_"endpoint" + 5# and #14 = y_"endpoint" -1# #x_"endpoint" = -11# and #y_"endpoint" = 15# The endpoint is #(-11,15)#